WASHINGTON (AP) — Democrats see a political winner in the stinging defeat they suffered when the Supreme Court ruled that businesses with religious objections may deny coverage for contraceptives under President Barack Obama’s health care law.

A four-term senator — Washington state’s Patty Murray — and a vulnerable freshman — Mark Udall of Colorado — have pushed legislation that would counter last month’s court ruling and reinstate free contraception for women who are on health insurance plans of objecting companies.

The Senate was expected to vote Wednesday on moving ahead on the bill, which backers have dubbed the “Not My Boss’ Business Act.” The White House expressed its strong support for the measure in a statement, saying it “believes that women should make personal health care decisions for themselves, rather than their employers deciding for them.”

Republicans who have endorsed the court’s decision as upholding the constitutional right of religious freedom are expected to block the measure.

The GOP has dismissed the bill as an election-year political stunt, designed to boost struggling incumbents. The contraception bill, Republicans say, has no chance of becoming law.

That hasn’t stopped Democrats from trying to use the issue to motivate female voters, crucial to the party’s hopes of keeping its tenuous Senate majority, in typically low-turnout midterm elections in November.

“Women across the country are watching,” Majority Leader Harry Reid, D-Nev., told reporters on Tuesday, leaving no doubt that GOP opposition will be part of an upcoming campaign ad or news release.

Countering the Democrats was Republican Sen. Kelly Ayotte, R-N.H., who stood with male GOP leaders and accused Democrats of peddling erroneous information about the impact of the court’s decision.

Nothing in it “allows a company to stop a woman from getting or filling a prescription for contraception,” Ayotte, one of four female GOP senators, told reporters.

On the Senate floor, female Democratic senators — and a few males — spoke out in support of the legislation as they warned of further discrimination against women and more changes in health coverage for millions. Democrats are counting on their argument resonating with female voters.

“Women should call the shots when it comes to their health care decisions,” Murray said.

National statistics from the Centers for Disease Control and Prevention show that more than 99 percent of women ages 15 to 44 who have had sexual intercourse have used at least one form of contraception.

“I trust women to make their own health care decisions, and I don’t believe their employers should have a say in them,” said Udall, who faces a tough race against Republican Rep. Cory Gardner in November.

In Colorado in 2008, female voters were critical to Udall’s election to the Senate, favoring his candidacy 56 percent to 41 percent while men backed him 50 percent to 46 percent, according to exit polls conducted by Edison Research for The Associated Press and other news organizations.

In the 2012 presidential election, Democrats overall captured the female vote by double digit margins as did the party in House races — 55 percent to 44 percent — as Obama won re-election. Democrats enjoyed a slightly better edge in the 2008 elections as Obama captured the presidency and Democrats maintained their congressional majority.

It was far different in the 2010 midterm elections, some eight months after Obama signed the health care law and as the tea party energized the GOP. Female voters backed Republicans 49 percent to the Democrats’ 48 percent, basically an even split, in a low-turnout election that enabled the GOP takeover of the House.

No wonder that on the other side of the Capitol on Tuesday, Democrats stood with various women’s groups to speak out for the legislation. They cast the Supreme Court decision in the case of Hobby Lobby, the Oklahoma-based chain of arts and craft stores that challenged the contraceptives provision, as five male justices on the court voting against the interests of women.

“I wish they could have had a conversation with their mothers, their wives, their daughters,” Minority Leader Nancy Pelosi, D-Calif., said.

Ilyse Hogue, president of NARAL Pro-Choice America, said the court’s decision has “awakened the pro-choice majority in this country.”

In Kentucky, NARAL launched a 30-second, black-and-white ad criticizing Senate Republican leader Mitch McConnell for his opposition to the legislation with the tag line, “Mitch McConnell will never do the right thing for Kentucky women.”

In one of the most closely watched races in the country, McConnell faces Democrat Alison Lundergan Grimes in his bid for a sixth term.

Answering critics of the GOP, McConnell has argued that the health care law has proven more harmful to women. He joined Ayotte and Sen. Deb Fischer, R-Neb., in backing a bill that reaffirms current law on access to contraception and calls for a Food and Drug Administration study on whether contraceptives could be sold over the counter without a prescription.

Sen. Lindsey Graham, R-S.C., said the Democratic bill is “just political messaging, inartfully done.” He said the Congress could be acting on plenty of legislation, but at the “end of the day, we’re doing nothing.”